A Unified Theory for the Great Plains Nocturnal Low-Level Jet

Abstract

Abstract A theory is presented for the Great Plains low-level jet in which the jet emerges in the sloping atmospheric boundary layer as the nocturnal phase of an oscillation arising from diurnal variations in turbulent diffusivity (Blackadar mechanism) and surface buoyancy (Holton mechanism). The governing equations are the equations of motion, mass conservation, and thermal energy for a stably stratified fluid in the Boussinesq approximation. Attention is restricted to remote (far above slope) geostrophic winds that blow along the terrain isoheights (southerly for the Great Plains). Diurnally periodic solutions are obtained analytically with diffusivities that vary as piecewise constant functions of time and slope buoyancies that vary as piecewise linear functions of time. The solution is controlled by 11 parameters: slope angle, Coriolis parameter, free-atmosphere Brunt–Väisälä frequency, free-atmosphere geostrophic wind, radiative damping parameter, day and night diffusivities, maximum and minimum surface buoyancies, and times of maximum surface buoyancy and sunset. The Holton mechanism, by itself, results in relatively weak wind maxima but produces strong jets when paired with the Blackadar mechanism. Jets with both Blackadar and Holton mechanisms operating are shown to be broadly consistent with observations and climatological analyses. Jets strengthen with increasing geostrophic wind, maximum surface buoyancy, and day-to-night ratio of the diffusivities and weaken with increasing Brunt–Väisälä frequency and magnitude of minimum slope buoyancy (greater nighttime cooling). Peak winds are maximized for slope angles characteristic of the Great Plains.